Chapter 10, Problem 4PS

(a)

To determine

To calculate: The parametric equations for the path of each plane if

The flight paths are $20°$ and $315°$.

One plane is $150$ miles from $P$ with a speed of $375$ miles per hour.

The other plane is $190$ miles from point $P$ with a speed of 450 miles per hour.

The figure is given below.

(b)

To determine

To calculate: The distance between the planes as a function of t if

The parametric equation of one of the planes:

$\begin{array}{l}{x}_1=\left(150-375t\right)\cos 70°\\ y_1=\left(150-375t\right)\sin 70°\end{array}$

The parametric equation of another plane:

$\begin{array}{l}{x}_2=\left(190-450t\right)\cos 135°\\ y_2=\left(190-450t\right)\sin 45°\end{array}$

(c)

To determine

To graph:

The function $y=\sqrt{{\left[\left(190-450t\right)\cos 135°-\left(150-375t\right)\cos 70°\right]}^2+{\left[\left(190-450t\right)\sin 45°-\left(150-375t\right)\sin 70°\right]}^2}$ and calculate the minimum distance between the planes and find if the planes keep a separation of at least 3miles.